Abstract
A high order spectral difference (SD) scheme based cost-effective multi-level optimization approach is proposed to optimize the kinematics of flapping airfoils and provide further insights into flapping motions with maximum propulsive efficiency. At the first stage, a gradient-based optimization algorithm is coupled with a second-order SD Navier-Stokes solver to search for the optimal kinematics of a certain airfoil undergoing a combined plunge and pitch motion. Then a high-order SD scheme is used to verify the optimization results and reveal the detailed vortex structures associated with the optimal kinematics of the flapping flight. Several NACA 4-digit airfoils are used in the optimization process. The maximum propulsive efficiency of oscillating NACA0006 and NACA0012 airfoils is more than 50% when the oscillating kinematics is optimized. The optimized propulsive efficiency of thin airfoils is larger than that of thick airfoils.
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